Find the Derivative - d/dx ((x+1)/(x-1))^2

Problem

d()/d(x)*((x+1)/(x−1))2

Solution

1. Apply the power rule and the chain rule by treating the inner fraction as the inner function.

d()/d(x)*((x+1)/(x−1))2=2*((x+1)/(x−1))⋅d()/d(x)(x+1)/(x−1)

2. Apply the quotient rule to differentiate the inner fraction (x+1)/(x−1)

d()/d(x)(x+1)/(x−1)=((x−1)⋅d(x+1)/d(x)−(x+1)⋅d(x−1)/d(x))/((x−1)2)

3. Evaluate the derivatives of the linear terms in the numerator.

d()/d(x)(x+1)/(x−1)=((x−1)*(1)−(x+1)*(1))/((x−1)2)

4. Simplify the numerator by distributing and combining like terms.

(x−1−x−1)/((x−1)2)=(−2)/((x−1)2)

5. Multiply the results from the chain rule application.

2*((x+1)/(x−1))⋅(−2)/((x−1)2)

6. Combine the terms into a single fraction.

(−4*(x+1))/((x−1)3)

Final Answer

d()/d(x)*((x+1)/(x−1))2=(−4*(x+1))/((x−1)3)

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